1. Field of the Invention
The present invention relates generally to methods of education and in particular to methods of self-education. More particularly, the present invention relates to a method of teaching oneself a large number of facts or principles about any one of a number of topics. More particularly yet, the present invention relates to such a method that enhances the retention of learned material in long-term memory. Even more particularly, the present invention relates to such a method that incorporates structured repetition of learned material, wherein the time interval between repeated presentations of already-learned material increases after each successful recall of that material, and conversely, wherein that time interval decreases upon an unsuccessful attempt to recall that material. Most particularly, the present invention relates to such a method that automatically optimizes the rules for each individual, determining when new material and previously learned material shall be presented, such a method that produces a continually evolving quantitative evaluation of the user""s success in learning the material targeted for acquisition.
2. Description of the Prior Art
Some aspects of teaching have remained relatively unchanged for many years. Nearly every educated person in modern society has experienced a classroom setting in which a teacher directs a group of students through a text about a particular topic. Through the decades, such classroom lessons have sought to instill knowledge through the assignment of individual work, often in the form of homework. After a pre-determined amount of material has been covered, a test is administered to measure the students"" retention of and proficiency with that material. After the test, the class moves on to cover new material, devoting no further attention to the already-covered material, with the possible exception of an end-of-term final exam containing a teacher-selected fraction of the material covered during the term.
It has long been observed that the structuring of the traditional educational program reflects a conflict of interest on the part of those maintaining it. By that, it is meant that the bodies such as school boards that have the responsibility for the education of young people have to meet goals that may not be consistent with applying the best teaching methods to the students. The most critical of these goals is to see that the educational program makes the most efficient use of scarce resources. That is, one wishes to develop and administer a program that benefits the greatest number of students affected by it. By its nature, the resulting program best serves the students with an average learning speed, and in so doing will short-change those students who learn at a faster or slower rate than the average. In summary, it is noted that the traditional mass-education program, in teaching an entire group of students at a pace that is optimal for the average student, will fail to recognize that students come to school from a wide range of backgrounds, bringing with them a wide range of learning aptitudes. Unless the individual student""s deviation from the norm is large enough to be immediately recognized, teachers generally do not respond to that individual student""s unique needs, a situation that might be partially alleviated were there easily obtained measures of each student""s progress. The present unsatisfactory approach to the non-average-student""s education is becoming increasingly harmful because of the rapidly increasing quantity and diversity of information that a student must assimilate in order to be even moderately well-educated. In passing, it can be noted that a particular student can be an above-average learner in one discipline, average in another, and below-average in a third. Even within a particular discipline, one may learn and retain some material quickly and yet stumble over other types of material, the latter being learned only with much repetition and effort.
The problem set out above is one that has certainly been recognized before. Since at least the 1960s, individualized courses of instruction have been designed with the goal of giving each student the opportunity to learn and to be tested at his or her own pace. Indeed, the phrase xe2x80x9cprogrammed instructionxe2x80x9d was coined during that period to refer to that method of instruction wherein the student progresses at his or her own rate. The student is presented with mini-exams every few pages and the results of those mini-exams determine the next set of material that is to be presented to the student. In general, these programmed courses allow the student to leave behind material once he or she has demonstrated a familiarity with it, again with the exception of a comprehensive examination at the end of a portion of the course.
Although programmed instruction was used long before personal computers were available to help implement it, the present ubiquity of such computers has led to their use with such material. For example, Ho et al. (U.S. Pat. No. 5,727,951; issued Mar. 17, 1998) discloses a computer-aided programmed learning system that allows the student to work at an individual pace. Seifert (U.S. Pat. No. 5,904,485; issued May 18, 1999) also discloses a computer-aided learning system that presents to the student material to be learned and assesses the student""s mastery of it. If mastery is lacking, the system of Seifert will present the material in a different way.
The methods disclosed by Ho et al. and Seifert and others of that school of thought all have the drawback that the material to be learned, once mastered, is not presented again. Such approaches ignore the fact that, even though material may be well-learned at one point, it can subsequently be lost. Thus, a drawback inherent in both traditional classroom methods and in traditional programmed instruction (whether computer-based or not) is the failure to allow for a student""s memory loss and/or confusion that develops over time following his or her one-time mastery of a certain body of knowledge. This failure is the more striking given the general agreement by researchers that a student is likely to have forgotten a large proportion of learned material within months or even weeks after the material has been xe2x80x9cmastered.xe2x80x9d Such rapid forgetting happens in spite of the fact that human memory is capable of retaining information over decades, indeed over lifetimes of 100 years and more.
To recognize and compensate for a fading memory of learned material, it might be thought that presenting the student periodically with information that he or she has already xe2x80x9clearnedxe2x80x9d might be useful. One effort in this direction is disclosed by Collins et al. (U.S. Pat. No. 5,577,919; issued Nov. 26, 1996), which provides for re-asking questions that have already been answered correctly. In the method of Collins et al. the student is presented with a set of facts and asked to divide it into a first group containing already-known items and a second group containing facts not-as-yet known. A sequence generator then presents a mix of items to the student from the first and second groups. This approach is then repeated, with new material being continually introduced. In this way, there is some re-presentation of already-learned material, and this will have the effect of enhancing the student""s long-term retention. The Collins et al. method, however, does not control the frequency with which known facts are re-presented to the student and in particular does not respond to the level of proficiency being demonstrated by the student in responding to the repeated presentation of questions.
Therefore, what is needed is a method of instruction that allows a student to learn at his or her own pace and that leads to longer retention of that which was once learned, be it in school, in on-the-job training, or while the student is working on his or her own. What is also needed is such a method that can provide the student or the student""s teacher with a quantitative measure of the student""s progress in learning particular items.
It is an objective of the present invention to provide a programmed method that will allow a student to work at his or her own individual pace and that enhances long-term retention of learned items to a greater extent than provided by traditional programmed instruction. It is a further objective of the present invention to provide such a method that will generate a quantitative measure of the student""s progress with respect to individual items being studied.
The present invention achieves the first of its objectives through a method of instruction that presents previously learned items to the student at a repetition rate that reflects the proficiency the student has shown in his or her knowledge of those items. In particular, the method of the present invention questions the student on previously learned items with a frequency that is inversely related to the student""s demonstrated proficiency in remembering those items. The present invention achieves the second of its objectives by analyzing this same demonstrated proficiency and storing the results of that analysis for review by the student or his or her teacher.
The method of the present invention can be directed at learning (memorizing) lists of factual information. It can also be used to develop skill in rule-manipulation that is often referred to as xe2x80x9cproblem solvingxe2x80x9d and to develop a demonstrable proficiency in the knowledge of scientific concepts. Nevertheless, for definitiveness, most the following discussion will envision the information to be learned to consist of a list of facts rather than principles or problems to be solved. Here, the associated questions, then, require only short factual answers. The questions presented or to be presented will be referred to as xe2x80x9cquestionsxe2x80x9d or xe2x80x9citems.xe2x80x9d The response given by the user will be referred to as a xe2x80x9cresponsexe2x80x9d or xe2x80x9canswer.xe2x80x9d The method will occasionally be referred to as including a xe2x80x9cProgram.xe2x80x9d This Program will be whatever moves the user and the test material through the various steps necessary to apply the method.
The person using the method of the present invention will be referred to herein as the xe2x80x9cuserxe2x80x9d or the xe2x80x9cstudent.xe2x80x9d A person working with or overseeing the student""s efforts will be referred to as the xe2x80x9cteacherxe2x80x9d or the xe2x80x9cproctor.xe2x80x9d For definitiveness and simplicity, this initial discussion will be predicated on there being a single session each day.
Archetypal examples of the first type of targeted learning (assimilating lists of facts) would be (1) solar system facts (e.g., masses of the sun and all the planets, distances between the solar system objects, materials comprising the planets and their moons, etc.), (2) geopolitical facts about the countries of the world, (3) breeds of dogs, (4) the periodic table including oxidation potentials of atoms, etc. Obviously, there is no end to such lists; the choice of the particular ones over which mastery will be attempted by a particular individual will depend on that individual""s personal interests and/or obligations. In such an application, the material presented will consist of simple questions requiring straightforward factual answers. The format of the questions can be, alternatively, (1) simple text in the language of the user, (2) language-independent images, or (3) any other means by which a question can be conveyed to a user. For that matter, the question may be conveyed by a combination of such forms. The choice will in part be determined by the nature of the list of facts being dealt with. In the dog-breeds example, the image of a representative of a particular breed would probably be the best way of determining whether the user can recognize and name that particular breed.
Pursuing further the variety of means by which questions are presented in the method and answers given by the user, it is noted that modern electronic techniques, including those currently under development, vastly expand the range of these means. As a simple extension of the means discussed above, consider a computer-based approach to giving hints in the context of a list of geopolitical facts about the world""s countries, and in particular the item: What is the capital of France? The question could be presented in exactly that textual form. On the other hand, it might be presented by showing the user a map of France, with the location of Paris marked; it might be presented by showing one or more photographs taken within the City of Paris, starting with general street scenes and leading up to an image of Notre Dame or the Eiffel Tower. Concurrently or alternatively, the computer system used for applying the method could generate the music for xe2x80x9cApril in Paris,xe2x80x9d or smells characteristic of Les Halles, and so on. Answers could be conveyed by the user via a keyboard, via a spoken word or words, and even, perhaps (in the future) by his or her brain waves being sensed by one of the peripheral components of the computer. Alternatively, in the case of questions dealing with the parts of an automobile engine, the correct response required to: Where is the carburetor? could be given by moving and clicking the computer mouse appropriately, and similarly for pointing out the parts of the human brain, in another type of list.
The heart of the present invention lies in its protocol for determining how frequently items that have already been answered successfully will be re-presented to the student. In this regard, the simplest embodiment of the present invention can be described as follows.
The first step in applying the method is to choose the master collection (xe2x80x9ccollectionxe2x80x9d) of items to be learned. At the first session the method will select from this collection of items in an order predetermined by the creator of the collection. Since by definition it is the first session, none of these items will have been presented before. Assume that the student works until N items have been seen, and that he or she responds well to M of the N items. Those M items will then be labeled in such a manner that they will not be asked until the next session, Session 2.
In the second session, first the M items answered well during the first session will be presented, and then the N-M items not answered well will be presented.
Of the M items first presented during the second session, assume that P are well-answered. Those P are then labeled so that they will not be re-asked on the third session but will be asked (presented) on the fourth. Assume that the remaining M-P items are answered only moderately well. They will be labeled so as to be re-asked on the third session. In this way, items that are well-answered are seen less and less often.
The time-ordering of the different categories of items on the second session, as discussed above, is reflective of the pattern that is most desirable to follow. It is important (though not a limiting element of the method of the present invention) that the items scheduled for re-asking at a particular session be presented prior to those not so queued. This is because of the importance of reinforcing the knowledge of those items and the fact that it is impossible to predict when a session is to be prematurely terminated. (The items that have never been asked have the lowest priority, and are reserved for the end of a given session.)
It is envisioned that the user will continue with an item until it is answered correctly; only then can he or she move on to the next item. Also, as part of this method, there will in general be available to the user a mode, call it a xe2x80x9cdictionary modexe2x80x9d in which the entire collection of items can be reviewed along with their correct responses.
In order to discuss the method of the present invention in somewhat more general terms, several more terms will be defined. xe2x80x9cNegative-Levelxe2x80x9d(xe2x80x9cN-Levelxe2x80x9d) Items or xe2x80x9cUnseen itemsxe2x80x9d will be those that have never been presented, and have L=xe2x88x921. xe2x80x9c0-Levelxe2x80x9d items are those that have been presented but have not been answered well enough to be queued for presentation in some future session, and have L=0. Finally, xe2x80x9cPositive-Levelxe2x80x9d (xe2x80x9cP-Levelxe2x80x9d) items or xe2x80x9cQueuedxe2x80x9d Items are defined as those items that are to be asked in a particular session, and have Lxe2x89xa70. In the context of these definitions, when the method is first applied to a new collection of items, all of the items in the collection are Unseen items. Gradually, as the student answers the items, they are shifted to the collection of 0-Level items and, if answered proficiently, to the collection of P-Level items.
Each item in the set of P-Level items has associated with it both a xe2x80x9ctime to next presentationxe2x80x9d (coded by means of a variable called the xe2x80x9cLevel,xe2x80x9d or xe2x80x9cLxe2x80x9d), and a session on which it is to be tested (its xe2x80x9cSession to Test,xe2x80x9d or xe2x80x9cStoTxe2x80x9d). If an item from that set is presented to the user, there are three possible outcomes. A poor response will result in the time to next presentation being cut in half, a response with medium accuracy will result in no change to that time, and a highly-accurate response will double the time to next presentation.
Although for the basic method of the present application to be applied, it is not necessary to adhere to this xe2x80x9cpowers-of-twoxe2x80x9d approach, this is a particularly convenient means of spacing out the re-asking of items in the P-Level collection. It is to be noted that each P-Level item, after being re-asked, may be labeled so as to be asked more frequently, less frequently, or remain unchanged.
All items, even those that are extremely simple, have associated with them an additional parameter, namely the xe2x80x9cScorexe2x80x9d of the particular item (always vis a vis the particular user, of course). In order to provide even more flexibility to the discussion, a raw score SR and a weighted score Sw will be introduced. In this context, SR is the score assigned to an item as a result of the user""s answer at a particular time and Sw is the score that the item receives once it is combined in some way with the Sw that the item had prior to being asked that time.
The Score, in turn, is used to determine whether L should change, as a function of two thresholds, a lower and an upper threshold. If the value of the weighted score Sw is above the upper threshold, the Level (L) of that item will be increased; should Sw fall between the upper and lower threshold L will remain constant, and should Sw fall below the lower threshold as the result of poor performance by the user during a particular presentation, L will be decreased. If L decreases to zero the item will be moved back into the set of O-Level items.
In order to be a bit more quantitative with respect to the embodiment of the method wherein the a particular P-Level Item is re-asked every second, every fourth, every eighth, . . . every xe2x80x9c2s thxe2x80x9d session (L=1, 2, 3 . . . .), one might define a quantity T that is equal to the number of sessions that must elapse until the particular item is re-asked.
T={2Lxe2x88x921xe2x88x921},
where L=1, 2, 3, . . . for a given P-Level Item. Thus for a P-Level Item having a Level of L=2, one session will be skipped between each time that the particular P-Level Item is asked. Similarly, if the Level for a particular P-Level Item is 8, then T=255, meaning that 255 sessions will pass before that particular P-Level Item is re-asked. If (as a result of one or more sessions in which a P-Level Item was not answered sufficiently correctly) L for that P-Level Item has fallen to 0, that item is no longer treated as a P-Level Item.
Now combine the concept of a P-Level Item""s score and its Level L. To be specific, one embodiment of the method has scoring as follows. A Score of 1000 is assigned to each P-Level Item being presented. Assume, then, that a completely correct answer leaves the P-Level item""s Score at 1000, that a completely incorrect answer reduces it to 0, and that partial credit can lead to any Score between 0 and 1000. Assume further that there exists a set of rules in this embodiment such that any item emerging from being presented with a Score of 800 or higher has its Level L incremented by unity, with a score of 699 or less has its Level L (given that L greater than 0) decremented by unity, and with any score in between has its L value unchanged. Consider, in that embodiment, a P-Level Item being presented with L=8. If it emerges with a Score of 800 or higher, its L will increase to 9, meaning that 255 sessions will pass before the Item is re-presented; if the Score is 699 or less, its L will decrease to 7, meaning that only 63 sessions will pass before this particular P-Level Item is re-presented; and for a Score between 700 and 799, L remains unchanged and the Item will be re-presented after 127 sessions have passed.
In a variant on the just-described embodiment, the score of a P-Level Item can be weighted by the scores of that P-Level Item at the ends of all previous presentations.
As part of the approach just described, one may assign a starting score of zero to an Unseen Item, only giving it a Level L and a T value once its score at the end of a particular presentation rises above a particular threshold level . Once the threshold score has been attained for an item, it is re-classified as a P-Level Item and is assigned a Level of 1.
Note that within the context of the above commentary, once an item has reached the threshold score and a Level L of 1, then, if this item (now a P-Level Item) is correctly answered the next time it is presented, L is again increased by 1. Consider a P-Level Item that has been correctly recalled each of three times it was re-presented (after the threshold score had been attained). It now has a Level L of 4, meaning that T={23xe2x88x921)=7. I.e., seven sessions will pass before it is re-presented. Alternatively stated, the P-Level Item will next be presented on the eighth session following the session in which its L value was increased to 4. The P-Level Item""s Level L continues to increase as the user continues to give the correct answer each time that that P-Level Item is presented and, consequently, the number of sessions between the current session and the next time the Item is presented increases geometrically. In contrast, the student""s failure to answer the P-Level Item correctly will cause its L to decrease. If, after its L has fallen to unity, the user again fails to respond correctly to the P-Level Item, the item in question will be placed in the set of 0-Level items and presented according to other rules.
Although the method of the present invention is not necessarily a computer-based method, the method""s scope is certainly expanded by the use of a personal computer or a computer terminal within a larger computer network. Needless to say, the use of a computer offers great advantages in managing the necessary calculations and bookkeeping tasks required for effective presentation of the Items and evaluations of their scores and of overall scores for the user. If a computer is used, some means of communication or interface between the computer and the user is necessary. The computer must be able to present questions either implicitly or explicitly to the user, and the user must have some means of providing the answer. The computer may present some combination of text, images, sounds (including music), smells, tastes, or any other modality to which the user can respond. The interface between computer and user may involve a keyboard, computer mouse, touch screen, voice recognition, or any other means of communication, including brain waves, small muscle movements or eye movements. A natural language interface may be feasible if the interface employs text or voice.
As alluded to previously, rules are employed that govern the selection of Items to be presented in a given session. For example, P-Level Items are presented before O-Level Items, and P-Level Items with lower levels are presented before those with higher levels. Unseen Items would normally be selected for presentation based on a logical order rule specific to the collection (e.g., using the earlier example of facts about the solar system, items dealing with the identity of the planets would be presented before items dealing with the chemical composition of individual planets), and a rule determines when a session number can be incremented. The purpose of these rules is to organize and present material to be learned so as to first enhance recall of material (P-Level Items) already in the user""s memory before presenting 0-Level Items, which in turn are presented prior to new material (Unseen Items) to be learned, and also to present material in a way that will complement other learning materials, such as a textbook.
It is possible to use other means to apply the method of the present invention; means such as flash cards with an indexing system, for example, can be used to present the items and to place items into the appropriate sets.
The present invention is a method of presenting material to be learned to a user in such a manner that new or not-yet-mastered material is presented to the user repeatedly until the user has attained a threshold degree of mastery of it. The xe2x80x9cmasteredxe2x80x9d material is then presented with ever-decreasing frequency, as long as the user continues to recall it. Thus, the user is queried on new and not-yet-mastered material at a relatively high frequency (in terms of sessions) and queried on old and mastered material in ever-decreasing frequency (increasing time intervals). This method of reiterative presentation of material that the user has demonstrated that he or she has learned enhances long-term retention. The method allows a student to work at his or her own pace. Furthermore, the method is efficient in that it presents the student with material that is not-yet-learned and does not unnecessarily present already-learned material, other than at controlled intervals as a means of enhancing long-term retention of that material. A complementary feature of the present invention is its score-keeping and performance tabulation permitting the student or the student""s teacher to monitor the student""s performance.